Question

Noelle stands at the edge of a cliff and drops a rock. The height of the rock, in meters, is given by the function f(x)=−4.9x2+17 , where x is the number of seconds after Noelle releases her rock.

Cesar, who is standing nearby on the ground, throws a rock straight up in the air. The height of Cesar’s rock, in meters, is given by the function g(x)=−4.9x2+13x , where x is the number of seconds after he releases his rock.

There is a moment when the rocks are at the same height.

What is this height?

Answer 1

For this case what we must do is to equal both functions at the moment in which it is to find the result.
We have then:
f (x) = g (x)
-4.9x2 + 17 = -4.9x2 + 13x
Clearing x we have:
17 = 13x
x = 17/13
x = 1.31 s
Then, to find the height, with respect to the floor we have:
g (1.31) = - 4.9 * (1.31) ^ 2 + 13 * (1.31)
g (1.31) = 8.62
Answer:
The height with respect to the ground is:
8.62 m

Answer 2

Answer: 8.62 meters

Explanation:

Given: The height of the rock, in meters, is given by the function
`f(x)=-4.9x^2+17` , where x is the number of seconds after Noelle releases her rock.

The height of Cesar’s rock, in meters, is given by the function
`g(x)=-4.9x^2+13x` , where x is the number of seconds after he releases his rock.

The moment when the rocks are at the same height then f(x)= g(x)

`\Rightarrow-4.9x^2+17=-4.9x^2+13x\\\\\text{Add }-4.9x^2\text{ ion both sides, we get}\\\\\Rightarrow\ 17=13x\\\\\Rightarrow\ x=(17)/(13)\\\\\Rightarrow\ x=1.3076`

To calculate height put x in first equation, we get

`-4.9(1.3076)^2+17=8.62189\approx8.62`

Hence, the height = 8.62 meters